A new finite element method is proposed to model the evolution of cracks in a 3D lattice under mechanical and thermal fatigue loading. This step-by-step method, based on the separation of initiation and propagation phenomenon, is tuned by fitted entrance parameters which command fatigue laws. It is founded on linear elasticity assumptions, and the crack's evolution is taken into account by a so-called element deletion method. After the algorithm of the model is presented, two examples of mechanical and thermal fatigue are considered. The evolutions of different crack network characteristic parameters as a function of the number of cycles is proposed and match, at least qualitatively, the general trends observed experimentally.